Question

In a recent survey of 10,300 randomly-selected U.S.adults,1,854 responded that they “the most common way I get my political and election news is through social media.”

(a) Calculate a point estimate for the proportion of all U.S. adults who primarily get their political news through social media.

(b) Calculate a 98% confidence interval for the proportion of all U.S. adults who primarily get their political news through social media.

(c) State the results of your calculation in a complete sentence that refers to the details of this example, as shown in the class notes.

(d) Explain what the phrase “98% confidence” means in the context of this example. Again, see class notes for examples.

(e) Based on your calculation, would it be fair to say that ”less than 1 in 5 U.S. adults primarily get their political and election news from social media”? Briefly explain.

Answer 1

a. Here p value is

b. z value for 98% CI is 2.326 as P(-2.326<z<2.326)=0.98

So Margin of ERror is

Hence CI is

c. Proportion of respondents who says that most common way they get their political and election news is through social media will lie in the range of 0.170 to 0.190

d. 98% confidence means we have 98% chances that population proportion lie in the range of 0.170 to 0.190

e. As 0.2 is not in the range of CI, it wont be fair to say that ”less than 1 in 5 U.S. adults primarily get their political and election news from social media”